Concept 13.1

Mean of Grouped Data

Source: NCERT Mathematics, Class 1010 minute lesson

Formal statement

For grouped data, the class mark of each class is its mid-point, (lower limit + upper limit)/2. The mean is x̄ = Σfᵢxᵢ / Σfᵢ, where xᵢ is the class mark and fᵢ the frequency.

The intuition

In the class 10–20 we don't know the exact values, only that 6 students fall somewhere inside. The fairest single stand-in is the middle, 15.

Using the lower limit, 10, pretends every value is at the bottom of its class and drags the mean down.

The attention

Look at the class mark: the middle of each class.

Class 10–20, frequency 6: use x = 15, not x = 10

Look hereNot here

Look here: The class mark, the middle. The class mark stands for all the values in its class. It sits in the middle, so errors above and below roughly cancel.
Not here: The lower limit. The lower limit is the easiest number to read off the table, but it biases every class downwards.
What it teaches: When you replace many values with one, choose the one that is fair to all of them.